Two Models of Nonadaptive Group Testing for Designing Screening Experiments

Nonadaptive algorithms for threshold group testing with inhibitors and error-tolerance

A group test gives a positive (negative) outcome if it contains at least u (at most l) positive items, and an arbitrary outcome if the number of positive items is between thresholds l and u. This problem introduced by Damaschke is called threshold group testing. It is a generalization of classical group testing. Chen and Fu extended this problem to the error-tolerant version and first proposed efficient nonadaptive algorithms. In this article, we extend threshold group testing to the k-inhibitors model in which a test has a positive outcome if it contains at least u positives and at most k-1 inhibitors. By using (d + k - l, u; 2e + 1]-disjunct matrix we provide nonadaptive algorithms for the threshold group testing model with k-inhibitors and at most e-erroneous outcomes. The decoding complexity is O(n(u+k) log n) for fixed parameters (d, u, l, k, e).

New construction for transversal design

The study of gene functions requires the development of a DNA library of high quality through much of testing and screening. Pooling design is a mathematical tool to reduce the number of tests for DNA library screening. The transversal design is a special type of pooling design, which is good in implementation. In this paper, we present a new construction for transversal designs. We will also extend our construction to the error-tolerant case.

Error-tolerant pooling designs with inhibitors

Pooling designs are used in clone library screening to efficiently distinguish positive clones from negative clones. Mathematically, a pooling design is just a nonadaptive group testing scheme which has been extensively studied in the literature. In some applications, there is a third category of clones called "inhibitors" whose effect is to neutralize positives. Specifically, the presence of an inhibitor in a pool dictates a negative outcome even though positives are present. Sequential group testing schemes, which can be modified to three-stage schemes, have been proposed for the inhibitor model, but it is unknown whether a pooling design (a one-stage scheme) exists. Another open question raised in the literature is whether the inhibitor model can treat unreliable pool outcomes. In this paper, we answer both open problems by giving a pooling design, as well as a two-stage scheme, for the inhibitor model with unreliable outcomes. The number of pools required by our schemes are quite comparable to the three-stage scheme.